Search

This paper is devoted to the formalisation problems of design knowledge used in business sys­tems, information systems, and software design. It discusses the notions of knowledge and informa­tion, introduces the concept of ``know-how'' knowledge, and proposes to use hierarchical finite state machines as the unified formalism to specify business systems, information systems, and software design strategies.

Aim of this paper is to estimate total of the crop of winter wheat in the skewed population of farmers in Lithuania using different sampling strategies, to compare the estimates with the true value, to compare the methods with each other and to find out the most suitable strategy for the estimation of the total.

In this paper it has been analyzed first line partial derivatives system, the line of which strongly degenerates. Transformation has been determined, which simplifies the system, i.e., the main matrix of a new system coefficients distinguish characteristics, that all matrix elements over or under main diagonal (except one) asymptotically equal zero.

The reseaches in analyticity of the modified L-functions are surveyed in the paper. The correc­tion of earlier result is made.

The teaching problems of independence of events are considered. In the paper the another that traditional method of teaching of independence of events is proposed.

The training of scientific generation of Lithuanian mathematicians is a vital objective of natio­nal significance. It is inseparable from general trends of training of scientific generation in Lithu­ania. This paper reviews the general dynamics of the number of scientists in all scientific fields. The scientific staff situation in mathematics, computer science and partly in mathematical educology is considered. The contribution of separate scientific and educational institutions into the training of generation is examined. General conclusions and recommendations are presented.

In the paper we present the results of integrated analysis of data stored in the system of the Lithuanian teacher's database and of data from other sources representing the state of education system and the demographical changes in Lithuania. The research covers the analysis of dynamics of pedagogical staff and pupils, and the prognosis of tendency that have impact on the development of information society. Special emphasis is placed on teachers of mathematics.

This paper presents the results of the intemational test in mathematics at the beginning of 2000–2001 academic year at LUA. Comparison between results of different countries are done. Some conclusions are discussed here too.

Various aspects of learning environments are discussed in the paper emphasizing the possibi­lities to improve teaching using them as a supplement of classroom-based teaching. Programming language C++ for Windows learning environment designed by the author is described.

Educational institutions are interested in attempting to increase the variety and number of course offerings by using alternative delivery systems including the Intemet. Implementing virtual learning environments is one of the ways to do so. This paper deals with results of questionnaire, which was made to identify advanced students and schoolchildren attitudes towards virtual learning environments.

In this paper we consider one-dimensional nonlinear Shrödinger equation. The equation inclu­des an absorption term and the solution is periodically amplified in order to compensate the lose of the energy. We present a finite difference approximation by a symetrical splitting scheme. The convergence of the discrete solution is proved.

In the paper we obtain the effective zero free regions for the Lerch zeta-function.

In the present paper we continue investigation of the local distribution of multiplicative ari­thmetic functions from the class M(G). A local theorem of large deviations is obtained.

In the paper the importance of the mathematical olympiads for the general development as well as for the actual state of education and training of mind and related problems are discussed. A review of the local net of Lithuanian olimpiads is made and especially the last achievments of the Lithuanian high school and University students in the World olympiads are analyzed.

In the paper some methods and ideas concerning the solving of non-formal mathematical prob­lems are discussed and investigated.

The paper deals with the analysis problem of transient heat distribution on the plate. The exter­nal surfaces of the plate are subject to the heat transfer by convection with time dependent fluid temperature. The efficiency of the numerical results is illustrated by the solution of the problem of a cooled plate.

The paper describes how to use dynamical links between Mathcad and Excel components. The usage of such dynamical data exchange is presented by solving of transportation problem.

Turbo Pascal is the main language used for teaching of algorithms in schools. However it is already outdated. Changes are needed. The paper discusses an alternative solution introducing Free Pascal into schools. The features of Free Pascal with respect to teaching of programming are analized. However the lack of acceptable interface with user remains the main obstacle to use Free Pascal for teaching purposes. The outline of a new interface designed for use in schools is presented. Problems of localization of Free Pascal and their solutions are presented as well.

The main aim of this paper is to identify current major trends in geometry and to discuss perspectives concerning its teaching in schools, for today and for tomorrow. Geometry involves three kinds of cognitive processes which fulfill specific epistemological functions: (1) visualization processes with regard to space representation for the illustration of a statement, for the heuristic exploration of a complex situation, etc.; (2) construction processes by tools: construction of figu­rations can work like a model; (3) reasoning in relationship to discursive processes for extension of knowledge, for proof, for explanation. The paper deals with relationship between geometry and computer technology. Among all school subjects, geometry stands as one which is bound to be influenced most profoundly by the recent progress both in hardware and software development. The purpose is to examine some influence of computer technology in the teaching and learning of geometry.

Mathematical models for decomposing and forecasting of time series are analysed in this paper. Sometimes we have the situations when we don't get good result describing time series by standard components (trend, cyclical, seasonal). It is often happened with economic indicators. For example, the method of evaluation is changed or economic crisis has happened. Inclusion of new variables – intervention variables – can help with these problems. There is investigation of model accuracy depending on accuracy of evaluation of different components. Time series of different structure were simulated for imitation of real situations. Estimation of time series models with intervention variables and traditional components was done by program Demetra.

One of the most sensitive indicators of a moral and social state of society is criminality. The paper examines the criminality trends in Lithuania in a respect of the East European countries. Dynamic series allows to decrease differences in crime registration systems and to distinguish the main trends in the rate of criminality. General tendencies of criminality in Lithuania are the same as in Bulgaria, Hungary or Poland. The analysis of differences between the criminality in Lithuania and the average criminality rates in Bulgaria, Hungary and Poland is fulfilled using linear regression model.

The models of study process data analysis and statistical software for decision-making support are presented in this paper. The models and software were developed using applied statistics met­hods (descriptive statistics, analysis of variance, nonparametric tests, cluster analysis, correlation and logistic regression analysis) as well as data warehousing, multidimensional reporting, visua­lisation, object progranuning technologies and software SAS. The developed system is used for the analysis of study process data of Kaunas University of Technology. It enables to analyse the relationships and dependencies between various factors (e.g. study areas, faculties, study modules groups, form of studies, credits, weighted averages of the exams grades, grades of study modules or their groups etc.) and use the results for the effective decision-making.

A constructive pseudoinverse operator forming algorithm is presented in the paper.

Long, almost 3500 years delay was observed, until the notion of positional number system originating from Babylon was introduced in Western Europe and, afterwards, in aIl over the modern world. This proves that acquaintance with such a complex concept as decimal fraction is must be started long before the arithmetic of decimal fractions is introduced. Teachers working experience using A. Bakštys and G. Bakštys textbook [5] in the 5-th grade is described in this paper.

In this paper we offer methods for estimation parameters of diodes of the Schottky by compa­ring outcomes of calculations and experiment. Definite some parameters of contact area: allocation of a active impurity in this area, to define more precisely a potential barrier in the area, to study tunnel mechanisms of electrons through this potential barrier. Such tasks are important from the practical point of view at improvement of performances of devices. One more problem the proce­dure helps to decide-to design devices with the established volt-ampere characteristic. In this case we can offer the corresponding allocation of an impurity in contact area, to select a technology for engineering of contact of the Schottky.

In this paper we offer method for estimation of the relaxation of a photoconductivity of high resistivity crystal, stimulate by laser impulse. The system of the six nonlinear ordinary differen­tial equations is solved. The relaxation of electrons across four most influential deep levels is ta­ken into account. Electron concentration changes on fifteen orders in a narrow boundary layer (0–5 × 10-8 s). In the sequent layers change of the electrons concentration is slower in the time interval up to 10-4 second. The system of the differential equations was solved by a method Gear with a modification of a step. The electro-optical parameters of the crystal we found out by the com­parison of calculation and experiment outcomes. From the other side it is possible to use calculation for improvement of the characteristics of the devices.

Quantitative tools for the budget in higher education have appeared in great number in last decade of last century. Two approaches of the mathematical modelling have appeared in higher education: the package model and locally designed model. Package models employ generalized re­lationships that are applicable to behavior in many different settings. These models seems to be the least utilized of the quantitative tools. Locally designed models simulate behavior or a process in a specific setting. This paper analyze one locally designed model – Vilnius University budget allo­cation (among departments) model. Calculations have been made using data of Vilnius University administration.

Paper discusses challenges to education called out by Educational delivery, Course manage­ment, Learning management and Authoring intelligence tutoring systems. Educational delivery systems – a software product or suite that facilitates the delivery of content or interaction by the web. Course management systems (CMS) – a software product that generally incorporates an educational delivery system for a topic (typically called a ``Course'' in educational institutions and most often facilitated via asynchronous-based formats) and provides integrated tools for measuring outcomes and reporting progress for individual or groups of students. CMS systems are currently most popular for educational institutions that are inclined to think of on-line development as course-centric. Learning management systems (LMS) – a software product that provides learners an integrated view of all their active coursework and assignments in a ``syllabus'' that spans multiple courses. LMS systems are most often found in large corporate training departments and corporate universi­ties. Intelligent management systems art computer-based instructional systems with models of inst­ructional content that specify what to teach, and teaching strategies that specify how to teach.

In the paper a survey of the activity of the seminar of the number theory is given.

In this paper the trivariate survival regression model for FGM family of distributions is const­ructed with marginal left-truncated logistic distributions. Two methods (using survival and hazard functions in the first case, and distributional density and ` `conditional'' survival function in the se­cond case) are used when constructing likelihood function for model parameter estimation. Const­ructed survival model was run with the data of the ` `KRIS'' (The Kaunas Rotterdam Intervention Study), which lasted for 22 years from 1972. The results show, that using second case for likehhood function construction gives better approximation for the data, because some additional conditions are considered.

Interpolating periodical splines estimation methods are considered in this paper. Periodical spli­ne universal implementation method is presented.

The purposes of this paper is to suggest aims and learning outcomes in teaching mathematical modelling and how to present material of the subject.

In the paper we discuss the visualization of multidimensional vectors taking into account the learning flow of the self organizing neural network. A new algorithm realizing a combination of the self-organizing map (SOM) and Sammon's mapping has been proposed. It takes into account the intermediate learning results of the SOM. The experiments showed that the algorithm gives lower average projection errors compared with a consequent application of the SOM and Sammon's mapping.

ECA rules implemented into database management systems (DBMS) as triggers have proven to be powerful and effective mechanisms to enforce business rules in applications. Collection of all business rules implemented in united repository of specific DBMS reduces efforts of implemen­tation and maintenance, so does uniform domain conceptual model. Several conceptual modelling languages might be used but we propose to use conceptual graphs (CGs) because CGs offer const­ructs for modelling all static and dynamic aspects of application domain in a uniform way, and have both, a standard representation, and a graphical notation. In this paper we propose a generic algo­rithm to generate database triggers from domain model represented by CGs. The algorithm uses Conceptual Graphs Interchange Format (CGIF) representation. Such usage of CGs for business rules modelling is advocated.

Research and results of the use of C++ Learning Environment for teaching at Vilnius Pedago­gical University are described in this paper. Results of questionnaires and Web Ct statistical data were used for the research.

In this paper the sequential variant of the additive arithmetic with equality and the non-logical symbols o, t, P, + , = is investigated and the proovable properties of the additional function nit is ascertained.

For theoretical and practical analysis of the self-thinning process we use stochastic differential equation, which take the form: dN (t) = N (t) (α - β ln N (t))dt + μN (t)dW (t), N(t0) = N0, t0 ≤ t ≤ T, where N – tree per hectare (stem/ha), t – stand age, W(t) – scalar standard Brownian motion, N0 – not random, α, β and μ are parameters – real constants. In this paper from a practical viewpoint we apply a simple numerical method for solution of the stochastic differential equations by the Milstein's higher order method. The programs for numerical simulation are written on MAPLE. The convergence of this model is explored too.

In this paper we consider the dependence of iterative methods convergence rate on iterative parameters selection. We propose the numerical algorithm determination of the optimal iterative parameters. Using it we solve classical minimization 2D and 3D problems and modificate 2D and 3D minimization problems and analyse the convergence rate dependence on the matrix spectral characteristics.

The paper deals with the problems of higher mathematics studies of the first course of the Mechanical Faculty students, analyses the results of the test in mathematics and presents thė ways to improve the studies.

We continue investigation of the local distribution of multiplicative arithmetic functions from the class M(G). In the present paper the local limit theorem of large deviations with asymptotical expansion of the principal term is obtained.

The paper analyses possibilities of using computer mathematics systems in teaching process. The work surveys possibilities of using systems by teachers. The advantages and disadvantages of such computer mathematics systems as MAPLE, MATHEMATICA, MATLAB and MATHCAD are also examined in the work.

Teaching of programming in secondary school raises some problems: how to teach program­ming, which language and environment to choose, what kinds of tasks to prepare, etc. The paper deals with these questions. The objective and component programming are briefly described as the most suitable for developing programming skills of students. The stages in teaching of prog­ramming are analyzed: basic computer skills, basic knowledge in programming, and developing of programs.

This paper discusses the computer literacy standard of students with respect to the European Computer Driving License (ECDL) and general informatics curricula of comprehensive schools. Some aspects of relations to ECDL Start modules are analyzed. The main attention is paid to discuss the virtue attitude of using the information and communication technology as well as to general capabilities related to computer literacy. The main propositions are presented and motivated. The paper also deals with the main fields of computer literacy topics: Basic principles and concepts of applying computers (1), Basics of information processing (2), Text handling and information presentation (3), Web and electronic mail (4), Introducing spreadsheet and data base (5), Social, juridical and ethical aspects (6).

This paper deals with the main problem of involving information technologies in education – contents of teachers' training courses. Three directions are presented: preparation of teachers (1), in-service teacher training (2), re-qualification of the speciality (3). The main attention should be paid to the constant in-service teachers' training. The Standard of computer literacy for educators has been developed. It should be the main sources of all teachers' training courses on informa­tion technology. The Standard consists of two parts: technological one and educational one. The technological part is based on ECDL Start modules. The educational part is uniqu: it requires some psychological, social, and pedagogical knowledge referring to information technology usage in education. The main attention of the paper is paid to the analysis and requirements of the educa­tional part of the Standard of computer literacy for educators.

The paper considers pollution spreading models, based on turbulent diffusion equation, as well as their numerical realization using particular data of rivers in Lithuania.

The paper deals with the problem of potential determination on a plain domain, using the con­formal mapping theory.

The paper deals with the discrete resource allocation problem and its application in the attack steering systems. The non-linear models of multiple target prioritisation are presented in the case of multiple different weapons. The fast greedy algorithms are presented and investigated. In the case of homogeneous resources (weapons) the algorithms give optimal solutions. The experiments show that the algorithms give sufficiently exact solutions in the case of different weapons.

In this paper we investigate one-dimensional stationary differential problems with various nonlocal boundary conditions and finite difference schemes for them. The boundary conditions of the first, second and third type are considered and nonlocal part of those boundary conditions can be integral type or Samarskii and Bitsadze type. The base idea is to use fundamental solutions of the stationary problems with classical boundary conditions. We find necessary and sufficient solvability conditions for such problems. Stability estimates are proved in the maximum norm. The convergence of the second order finite difference schemes is proved.

Flash estimation of GDP by production approach has been stated in Statistics Lithuania. Econometric methods are used for estimation of GDP components. The main problem is that time series are quite short and GDP is affected by results of work of single enterprises. That’s why it’s very important to know if the parameters of the models are stable or not. Main purpose of this paper is to evaluate stability of the GDP components models. This is done by generation of random series (with Gaussian and Student distributions) as a new residuals and recalculation of parameters with new dependent variables, which are equal to the already estimated model plus generated residuals. Main results of this work are quite satisfactory – new estimators are very close to first ones (most cases the error is less than 1 per cent). Exceptions are only the time series where residuals had outliers. Suggestion is to evaluate outliers prior to parameters estimation.

Theoretical and practical aspects of construction splines curves and surfaces with MATLAB are discussed in this paper.